A Bayesian approach to the mean flow in a channel with small but arbitrarily directional system rotation

Abstract

The logarithmic law of the wall loses part of its predictive power in flows with system rotation. Previous work on the topic of mean flow scaling has mostly focused on flows with streamwise, spanwise, or wall-normal system rotation. The main objective of this work is to establish the mean flow scaling for wall-bounded flows with small but arbitrarily directional system rotation. Our approach is as follows. First, we apply dimensional analysis to the Reynolds-averaged momentum equation. We show that when a boundary-layer flow is subjected to small system rotation, the constant stress layer survives, and the mean flow U+ is a universal function of y+, Ωx+, Ωy+, and Ωz+, where U is the mean flow, y is the distance from the wall, Ωi is the system rotation speed in the ith direction (in the locally defined coordinate), and the superscript + denotes normalization by the local wall units. Second, we survey the three-dimensional parameter space of Ωx,y,z+ and determine U+(y+,Ωx+,Ωy+,Ωz+) for small Ω+. Here, we conduct direct numerical simulation (DNS) of a Reτ = 180 channel at various rotation conditions. This approach is conventionally considered as “brutal force.” However, as we will show in this work, the Bayesian approach allows us to very efficiently sample the parameter space. Four independent surveys are conducted with 146 DNSs, and the resulting Bayesian surrogate agrees well with our DNSs. Finally, we upscale to high Reynolds numbers via wall-modeled large-eddy simulation. In general, the present framework provides a path for surrogate modeling in a high-dimensional parameter space at high Reynolds numbers when sampling in a designated parameter space is possible at only a few conditions and at a low Reynolds number.